Solve 3x^4-81x

$$3 x ^ { 4 } - 81 x$$

Factor

$$3x\left(x-3\right)\left(x^{2}+3x+9\right)$$

Solution Steps

Factor out 3.

$$3\left(x^{4}-27x\right)$$

Consider x^{4}-27x. Factor out x.

$$x\left(x^{3}-27\right)$$

Consider x^{3}-27. Rewrite x^{3}-27 as x^{3}-3^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

$$\left(x-3\right)\left(x^{2}+3x+9\right)$$

Rewrite the complete factored expression. Polynomial x^{2}+3x+9 is not factored since it does not have any rational roots.

$$3x\left(x-3\right)\left(x^{2}+3x+9\right)$$

Evaluate

$$3x\left(x^{3}-27\right)$$